This invention relates to determination of parameters of subsurface formations and, more particularly, to an apparatus and method for determining the water-filled porosity of formations surrounding a borehole.
A number of techniques presently exist for determining the porosity of subsurface formations. Typically, electrical, sonic, and/or nuclear logging devices are lowered into a borehole and information from one or more of these devices is utilized to obtain a measure of the porosity of subsurface formations. Typically, readings or samples indicative of other subsurface parameters, for example lithology and saturation of fluids, is also determined, and the determination of porosity is made using a combination of available information.
There are a number of different porosity parameters, and it is generally useful to obtain information about each one, if possible. Total porosity, designated .phi..sub.t, generally means the total fraction of formation unit volume which is occupied by pore spaces or interstices. Water-filled porosity, designated .phi..sub.w, is the fraction of the formation unit volume occupied by water, and hydrocarbon porosity, designated .phi..sub.hc, is the fraction of formation unit volume occupied by hydrocarbons. Generally, .phi..sub.t equals the sum of .phi..sub.w and .phi..sub.hc. It is evident that in situations when two of these three porosity parameters are known with reasonable reliability, valuable conclusions can be drawn concerning the nature of the subsurface formations under investigation. It is also known that comparison of porosity determinations from different logging devices, even ones which supposedly yield information concerning the same porosity parameter, can be highly useful in determining the nature of subsurface formations. Accordingly, it would be useful to have an additional reliable measure of a porosity parameter, such as .phi..sub.w, which will typically be utilized in conjunction with other logging information in visualizing the overall nature of subsurface formations traversed by a borehole.
In the U.S. Pat. No. 3,944,910 of Rama Rau there is disclosed an apparatus for injecting microwave electromagnetic energy into subsurface formations to investigate properties of the formations. The Rau patent discloses, inter alia, a technique for determining the loss-corrected velocity (where velocity is inversely related to travel time) of microwave electromagnetic energy propagating through subsurface formations. For lossless media, the velocity of propagation of electromagnetic energy is inversely proportional to the square root of the dielectric constant. A velocity correction is generally made, however, when the propagating media exhibits lossiness.
It has been proposed that water-filled porosity of a subsurface formation, consisting of water in a matrix, could be determined by obtaining the loss-corrected velocity of the formation, and then utilizing a time-average relationship to determine the water-filled porosity. In particular, the following relationship has been set forth: EQU .sqroot..epsilon..sub.corr = (1 - .phi..sub.w) .sqroot..epsilon..sub.m + .phi..sub.w .sqroot..epsilon..sub.wo ( 1)
where .epsilon..sub.corr represents the loss-corrected dielectric constant of the formations, .epsilon..sub.wo is the dielectric constant of lossless water, and .epsilon..sub.m is the dielectric constant of the formation matrix. .epsilon..sub.corr can be obtained using the techniques set forth in the referenced Rau patent. .epsilon..sub.wo is determinable, for a particular frequency and temperature, experimentally in the laboratory. If lithology is known, .epsilon..sub.m of the matrix, generally assumed to be lossless, is also known. The square root of dielectric constant is inversely proportional to velocity, so the relationship (1) is in a time-average form. Relationship (1) indicates that the composite velocity is expressed as an average of the velocity in the water multiplied by the fractional volume of water plus the velocity in the matrix multiplied by the fractional volume of the matrix. All terms in the relationship (1) consider the various propagation media (matrix, fluid, and composite) as being lossless, bearing in mind that the measured dielectric constant has been loss-corrected in this expression. Solving for .phi..sub.w yields: ##EQU1##
It is an object of the present invention to provide an apparatus and method which yields a determination of water-filled porosity which is an improvement over prior art techniques, such as the one relating to expression (2).